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Routing of Strategic Passengers in a Transportation Station

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Performance Engineering and Stochastic Modeling (EPEW 2021, ASMTA 2021)

Abstract

We study the routing decisions of passengers in a transportation station, where various types of facilities arrive with limited seating availability. The passengers’ arrivals occur according to a Poisson process, the arriving instants of the transportation facilities form independent renewal processes and the seating availability at the successive visits of the facilities correspond to independent random variables, identically distributed for each facility. We analyze the strategic passenger behavior and derive the equilibrium strategies. We also discuss the associated social welfare optimization problem.

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References

  1. Afimeimounga, H., Solomon, W., Ziedins, I.: The Downs-Thomson paradox: existence, uniqueness and stability of user equilibria. Queueing Syst. 49(3–4), 321–334 (2005)

    Article  MathSciNet  Google Scholar 

  2. Afimeimounga, H., Solomon, W., Ziedins, I.: User equilibria for a parallel queueing system with state dependent routing. Queueing Syst. 66(2), 169–193 (2010)

    Article  MathSciNet  Google Scholar 

  3. Altman, E., Ayesta, U., Prabhu, B.J.: Load balancing in processor sharing systems. Telecommun. Syst. 47(1–2), 35–48 (2011)

    Article  Google Scholar 

  4. Ayesta, U., Brun, O., Prabhu, B.J.: Price of anarchy in non-cooperative load balancing games. Perform. Eval. 68(12), 1312–1332 (2011)

    Article  Google Scholar 

  5. Bell, C.E., Stidham, S., Jr.: Individual versus social optimization in the allocation of customers to alternative servers. Manag. Sci. 29, 831–839 (1983)

    Article  Google Scholar 

  6. Bountali, O., Economou, A.: Equilibrium joining strategies in batch service queueing systems. Eur. J. Oper. Res. 260, 1142–1151 (2017)

    Article  MathSciNet  Google Scholar 

  7. Bountali, O., Economou, A.: Equilibrium threshold joining strategies in partially observable batch service queueing systems. Ann. Oper. Res. 277, 231–253 (2019)

    Article  MathSciNet  Google Scholar 

  8. Bountali, O., Economou, A.: Strategic customer behavior in a two-stage batch processing system. Queueing Syst. 93, 3–29 (2019)

    Article  MathSciNet  Google Scholar 

  9. Calvert, B.: The Downs-Thomson effect in a Markov process. Probab. Eng. Inf. Sci. 11(3), 327–340 (1997)

    Article  MathSciNet  Google Scholar 

  10. Canbolat, P.G.: Bounded rationality in clearing service systems. Eur. J. Oper. Res. 282, 614–626 (2020)

    Article  MathSciNet  Google Scholar 

  11. Cohen, J.E., Kelly, F.P.: A paradox of congestion in a queuing network. J. Appl. Probab. 27(3), 730–734 (1990)

    Google Scholar 

  12. Czerny, A.I., Guo, P., Hassin, R.: Hide or advertise: the carrier’s choice of waiting time information strategies (2018). Preprint available at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3282276

  13. Economou, A., Manou, A.: Equilibrium balking strategies for a clearing queueing system in alternating environment. Ann. Oper. Res. 208, 489–514 (2013)

    Article  MathSciNet  Google Scholar 

  14. Edelson, N.M., Hildebrand, K.: Congestion tolls for Poisson queueing processes. Econometrica 43, 81–92 (1975)

    Article  MathSciNet  Google Scholar 

  15. Grossman, T.A., Jr., Brandeau, M.L.: Optimal pricing for service facilities with self-optimizing customers. Eur. J. Oper. Res. 141(1), 39–57 (2002)

    Article  MathSciNet  Google Scholar 

  16. Hassin, R.: Rational Queueing. CRC Press, Taylor and Francis Group, Boca Raton (2016)

    Book  Google Scholar 

  17. Hassin, R., Haviv, M.: To Queue Or Not to Queue: Equilibrium Behavior in Queueing Systems. Kluwer Academic Publishers, Boston (2003)

    Book  Google Scholar 

  18. Logothetis, D., Economou, A.: The Impact of Information on Transportation Systems with Strategic Customers (2020). Preprint

    Google Scholar 

  19. Kulkarni, V.: Modeling and Analysis of Stochastic Systems, 2nd edn. CRC Press, Boca Raton (2010)

    MATH  Google Scholar 

  20. Manou, A., Canbolat, P.G., Karaesmen, F.: Pricing in a transportation station with strategic customers. Prod. Oper. Manag. 26, 1632–1645 (2017)

    Article  Google Scholar 

  21. Manou, A., Economou, A., Karaesmen, F.: Strategic customers in a transportation station: when is it optimal to wait? Oper. Res. 62, 910–925 (2014)

    Article  MathSciNet  Google Scholar 

  22. Naor, P.: The regulation of queue size by levying tolls. Econometrica 37, 15–24 (1969)

    Article  Google Scholar 

  23. Orda, A., Rom, R., Shimkin, N.: Competitive routing in multiuser communication networks. IEEE/ACM Trans. Netw. 1(5), 510–521 (1993)

    Article  Google Scholar 

  24. Patriksson, M.: The Traffic Assignment Problem: Models and Methods. Courier Dover Publications, New York (2015)

    Google Scholar 

  25. Peressini, A.L., Sullivan, F.E., Uhl, J.J.: The Mathematics of Nonlinear Programming, pp. 10–13. Springer-Verlag, New York (1988)

    Book  Google Scholar 

  26. Richman, O., Shimkin, N.: Topological uniqueness of the Nash equilibrium for selfish routing with atomic users. Math. Oper. Res. 32(1), 215–232 (2007)

    Article  MathSciNet  Google Scholar 

  27. Roughgarden, T., Tardos, É.: How bad is selfish routing? J. ACM (JACM) 49(2), 236–259 (2002)

    Article  MathSciNet  Google Scholar 

  28. Stidham, S., Jr.: Stochastic clearing systems. Stoch. Process. Appl. 2, 85–113 (1974)

    Article  MathSciNet  Google Scholar 

  29. Stidham, S., Jr.: Optimal Design of Queueing Systems. CRC Press, Taylor and Francis Group, Boca Raton (2009)

    Book  Google Scholar 

  30. Wardrop, J.G.: Some theoretical aspects of road traffic research. Proc. Inst. Civ. Eng. 1(3), 325–362 (1952)

    Google Scholar 

  31. Whitt, W.: Deciding which queue to join: some counterexamples. Oper. Res. 34(1), 55–62 (1986)

    Article  MathSciNet  Google Scholar 

  32. Wolff, R.: Poisson arrivals see time averages. Oper. Res. 30, 223–231 (1982)

    Article  MathSciNet  Google Scholar 

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Acknowledgement

D. Logothetis was supported by the Hellenic Foundation for Research and Innovation (HFRI) under the HFRI PhD Fellowship grant (Fellowship Number: 1158.). We cordially thank the three anonymous reviewers for their constructive remarks on the initial revision of the paper.

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Correspondence to Dimitrios Logothetis .

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Logothetis, D., Economou, A. (2021). Routing of Strategic Passengers in a Transportation Station. In: Ballarini, P., Castel, H., Dimitriou, I., Iacono, M., Phung-Duc, T., Walraevens, J. (eds) Performance Engineering and Stochastic Modeling. EPEW ASMTA 2021 2021. Lecture Notes in Computer Science(), vol 13104. Springer, Cham. https://doi.org/10.1007/978-3-030-91825-5_19

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  • DOI: https://doi.org/10.1007/978-3-030-91825-5_19

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  • Online ISBN: 978-3-030-91825-5

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